# Canadian First Class ME Applied Heat

##### Brought to you by www.dieselduck.net comments to [email protected]
###### Transport Canada has ask us to advise users of this webpage to keep in mind that these questions are not the exact questions found in their exams. Martin's Marine Engineering Page - www.dieselduck.net is not affiliated with Transport Canada and these questions have been gathered from various sources.

CR of BC, in March 2010, reports " BTW just wanted to inform you that I recently wrote my 1st class Thermodynamic and all 9 questions came form this site."

1.  A vessel containing 19.5 kg of water at a temperature of 89oC has 18kg of ice at a temperature of -13oC placed inside. Neglecting the effect of the containing vessel and loss due

1) The equilibrium temperature.

2) The amount of the mixture that must be removed and heated to 100oC so that when it is replaced, the final temperature will be 10oC.

note:

Specific heat capacity of water = 4.187 kJ(kgK)-1

Specific heat capacity of ice   = 2.11  kJ(kgK)-1

Enthalpy of fusion of ice, = 336 kJ/kg

Ans:4.62oC Ans:2.12 kg

2.  Three different liquids each of mass x, y and z have equal volumes, identical specific capacities and are at temperatures of 49oC, 63oC and 80oC respectively.  If x is mixed with y the resulting temperature is 54oC.  If y is mixed with z the resulting temperature is 69oC. Calculate the final or equilibrium temperature when all three liquids are mixed in the mass ratios of 2, 3 and 5 respectively

Ans: 62.57oC

Ref DOT2 Ref Reeds p24 ,p284 (similar)

3.  The load on a single collar type of thrust block is 250 kN at a shaft speed of 100 rev/min and the mean diameter of the thrust pads is 480 mm.  The coefficient of friction between collar and pads is 0.03 and the lube oil increases in temperature by 20oC.  Calculate:

1) the power lost due to friction

2) the heat energy generated per hour

3) the mass flow of oil (kg/h) required to limit the temperature rise to 20oC

note: specific capacity of oil = 2 kJ(kgK)-1

Ans: 18.85 kW Ref DOT3

Ans: 67.86 MJ Ref Reeds p23 and 288 #4

Ans: 1696.5 kg/h

4.  Calculate the equilibrium temperature resulting from the mixture of 41 kg of ice at -25oC, 61 kg of water at 65oC and 64 kg of water at 62oC.  Neglect the effect of the containing vessel.

note: specific heat capacity of water = 4.187 kJ(kgK)-1

note: specific heat capacity of ice = 2.11 kJ(kgK)-1

note: enthalpy of fusion of water = 336 kJ/kg

Ans: 24.86oC

5.  Calculate the rise in temperature of 4000 l of water at 45oC when 50 kg of dry steam at a pressure of 900 kPa are blown into it.

note: the specific heat capacity of water = 4.187 kJ(kgK)-1

Ans: 7.6oC Ref DOT5

6. A calorimeter has a water equivalent of 250 g. and mass of water in the calorimeter is 1.5 kg. When 1.57 g. of fuel are burnt in the calorimeter, the temperatures of the metal and the water rise by 5.6oC.  Calculate the heating value (calorific value) of the fuel (MJ/kg).  Specific heat of water = 4.187 kJ/kg.K.

Ans: 26.1 MJ/kg. Ref. DOT6.

7. The bi-metallic element of a control device consists of two thin flat strips, one of a nickel and the other of aluminum, the ends of which are fastend together a distance of 50 mm by means of two brass spacers 2.5 mm long. Calculate the radius of the curvature of the assembly when the

temperature is increased by 200oC.

note:

alpha Aluminum =(22.5 x 10-6)/K

alpha Nickel   =(12.8 x 10-6)/K

alpha Brass    =(18.0 x 10-6)/K

Ans: 1296.5 mm

Ans: 1299.11 mm

8.  A copper steam pipe of outside diameter 80 mm, inside diameter 65 mm and length 3.85 m is at a temperature of 85oC. Both ends of the pipe are securly fixed to restrain contraction and expansion.  Calculate:

1) the stress in the pipe when it cools to a temperature of 65oC

2) what total force applied to the ends of the pipe would cause the same stress

note: linear expansion coefficient of copper = (16.7)(10-6)K

note: modulus of elasticity = 116 GPa

Ans: 38.744 MPa Ref DOT8

Ans: 66.18 kN

9.  A steam pipe has fractured due to the malfunction of and expansion gland.  The operating temperature of the pipe was 200oC but the pipe had cooled to 22oC when the crack occured.  The length was measured at this latter temperature and found to be 4.42 m.  A temsile test specimen taken from the pipe fractured at 423.4 MPa.  Calculate the modulus of elasticity of the pipe material.

note: linear expansion coefficient of pipe material =(12x10-6)K

Ans: 198.221 GPa Ref DOT9

10. A solid metal sphere at a temperature of 15oC. is placed in 100 litres of fresh water at a temperature of 95oC. It was found that when equilibrium conditions prevailed, the diameter of the sphere had increased by 0.15%.  Calculate the original diameter of the sphere.

note: specific heat capacity of water = 4.187 kJ(kgK)-1

note: specific heat capacity of sphere = 0.8876 kJ(kgK)-1

Linear expansion coefficient of sphere = 23(10-6)/K.

Relative density of sphere material at 15oC. = 2.56.

Ans. 43.07 cm. Ref. DOT10.

11. A glass beaker contains 125 ml of mercury at a temperature of 20oC.  Calculate the quantity of mercury that will overflow when both beaker and mercury are heated at 80oC.

Note:

Coeff. of linear exp. (glass) alpha = 8.5(10-6)/K

Coeff. of volumetric exp. (mercury) beta = 1.8(10-4)/K.

Ans: 1.59 ml.

12.  A telemotor system consists of two (2) copper popes each 80 mm long, 15 mm inside diameter, completely filled with hydraulic fluid at a temperature of 16oC.  Calculate the quantity of fluid (dm3) released to the replenishing tank when the temperature rises to 40oC.  Disregard the quantity in the hydraulic cylinders.

note: coefficient of linear expansion (copper) = 1.7 x 10-5/K

note: coefficient of volum expansion (fluid) = 7.7 x 10-4/K

Ans: 0.4879 Ref DOT12

13.  Flue gas at a temperature of 290oC and air at a temperature of 40oC flow on either side of a metal plate 5 mm thick.

note: The heat transfer coefficient of the gas is 30.5 Wm-2K-1

note: the thermal conductivity coefficient of the metal plate is 40 W(mK)-1

Calculate:

1) the overall heat transfer coefficient

2) for a 1 m2 area, the heat transfer from gas to air per minute

Ans: 15.59 W/m2K Ref DOT13

Ans: 233.85 kJ/min

14. A spherical vessel of 1 m diameter, contains a liquified gas at a temperature of -180oC.  The vessel is lagged to a thickness of 200 mm with insulating material having a coefficient of thermal conductivity of 0.05 W(mK)-1. Calculate the heat transfer per second through the insulation if the surface temperature is 15oC.

Ans.214.4 Watts or J/s.    Ref DOT14

15.  Steam at a pressure of 3000 kPa. and a tempeature of 500oC. flows through a 150 mm. Diameter pipe which is covered with lagging to a diameter of 300 mm.  The temperature of the

outer surface of the lagging is 50oC. and the thermal conductivity coefficient of the lagging is 0.6W(mK)-1. Calculate the energy lost per second from a 50 metre length of the pipe.

Ans. 122.373 kW Ref. DOT15.

16.  The inner wall of a cold storage chamber is maintained at a temperature of -2oC when the outside wall temperature is 21oC.  The chamber wall is constructed of a 110 mm thickness brick, a 75 mm thickness of corkboard and a 25 mm thickness of wood whick is applied to the interior wall, the brick forming the interior surface.  The thermal conductivities of brick, corkboard and wood are 0.95; 0.043 and 0.17 W(mK)-1 respectively. Calculate:

1) the heat transfer (kJ) through 1 m2 of wall during a 24 hour period

2) the interface temperatures

Ans: 990 kJ/day

Ans: 19.315oC

Ans: -0.673oC

17.  The temperatures at the outside surfaces of a furnace wall are 1120oC and 150oC respectively.

1) Calculate the heat transfer (kJ/h) through 1 m2 of the wall if it is constructed of refractory brick and is 340 mm thick.

2) Determine the reduction in the amount of heat lost if 100 mm of insulating brick are now added to the wall. In this case the surface temperatures are 1120oC and 23oC respectively

note: lambda (refractory brick) = 0.7 W(mK)-1

note: lambda (insulating brick) = 0.25 W(mK)-1

Ans: 7189.4 kJ/h Ref DOT17

Ans: 2730.6 kJ/h

18. 1) Two layers of differant material of thickness L1, and L2 and thermal conductivities lamda1 and lamda2 are placed in close contact with each other. Deduce from first principles an expression for the heat transfer through this composite structure.

2) A wall consists of a external layer of brick 500mm thick to which is fastened a cork board layer 80mm thick. The thermal conductivity of the brick is 0.5 W(mK)-1 and the corkboard, 0.048 W(mK)-1.

Calculate the heat transfer through 1m2 of wall each hour if the temperature difference between the inner and outer surfaces is 50oC.

Ans: Q = A t (delta T) Sumation ( s  ) lambda

Ans: 67.5[kj/hr]

19. A Fortin barometer registers 720 mm  Hg, the vacuum gauge indicates 715 mm  Hg  and the temperature inside the condenser is 32oC.  Air is extracted from the condenser at the rate of 3.85 m3/min.  Calculate:

1) the quantity of air leaking into the condenser (kg/min)

2) the quantity of steam vapour associated with the air (kg/min)

note: Assume the standard atmosphere = 100 kPa

note: R (air) = 0.287 kJ(kgK)-1

Ans: 0.1721 kg/min

Ans: 0.1302 kg/min

20.  A tank having an internal volume of 4 m3 contains gas at a temperature of 20oC, a pressure of 6 kPa and a gas constant, R = 0.27 kJ(kgK)-1.  Another gas having a mass of 0.4 kg, a temperature of 20oC, and a gas constant, R = 0.28 kJ(kgK)-1, is introduced into the tank.  Calculate:

1) the mass of gas initially in the tank

2) the final pressure of the mixture of the gasses

Ans: 0.3792 kg Ref DOT20

Ans: 12.5632 kPa

21.  A condenser has a volume of 20 m3 and contains a mixture of air and dry saturated steam at a total pressure of 9 kPa and a temperature of 38oC.  Calculate:

1) the mass of steam in the vesse

2) the mass of air in the vessel

3) the mass ratio of the air to steam

Ans: 0.9246 kg Ref DOT21

Ans: 0.5322 kg

Ans: 0.5756

22.  1)  State Daltons Law of Partial Pressures

2)  A closed vessel of 500 cm3 capacity contains a sample of flue gas at 101 kPa. and 20oC.  If the sample of the flue gas by volume is 10% Carbon Dioxide, 8% Oxygen and 82% Nitrogen, calculate the partial pressure and mass of each constituent in the sample. R  for CO2, O2 and N2 = 0.189, 0.26, and 0.297 kJ(kgK)-1 Ans.  Partial pressures, CO2 = 10.15 kPa, O2 = 8.12 kPa.                   N2. = 83.23 kPa.

Masses: CO2 = 0.09164 g.

O2. = 0.0533 g.

N2. = 0.4782 g.

23.  1) The quantity or amount of a substance is known as the mole (mol).  How has the mol been defined under the System International d'Unites (S.I.)

2) Calculate the gas constant R for Oxygen

note: Relative atomic mass of Oxygen = 16

note: Universal gas constant Ro = 8.3143

Ans: The mole is more commonly referred to as the kilogram-mole (kg-mol) and defined as a quantity of gas equivalent to "m" kg of the gas, where "m" is the molecular weight of the gas.  For example the molecular weight of Oxygen is 32 therefore the mass of one kg-mol of Oxygen is 32 kg.  The molecular weight of hydrogen is 2.  Hence one kg-mol of hydrogen is a mass of 2 kg. etc.

Ans: 0.26 kJ(kgK)-1  Ref DOT23

24. 1) State Avogadro's law and also state the approximate number value of Avogadro's number.

2) An experiment shows that an average value for the volume of 1 mol of a permanent gas is 22.4136m3 at standard atmospheric pressure, 101.325 kPa. and 0oC.

Calculate the Universal Gas Constant, Ro

note: T=0oC = 273.15 K

Ans: 6.022 (10)23 molecules/mol

Ans: 8.3143 kJ/molK

25.  A gas at the start of compression, has a pressure of 100 kPa a temperature of 20oC and a volume of 9600 cm3.  At the end of compression the temperature is 512oC and the volume is

720 cm3.  Calculate:

1) the compression index "n"

2) the work done during the compression process (kJ)

3) the change of internal energy (kJ)

4) the heat transfer during compression (kJ)

note: specific heat capacity cv = 0.657 kJ(kgK)-1

note: R(gas) = 0.264 kJ(kgK)-1

note: area under compression curve PVn = (P1V1 - P2V2)/n-1

Ans: 1.38 Ref DOT25

Ans: -4.242 kJ

Ans: 4.011 kJ

Ans: -0.231 kJ

26.  Derive the following expression which gives the heat supplied during a polytropic expansion process. Q. = (gamma - n) W (gamma - 1)

where; Gamma = adiabatic index, n = polytropic index, W = work done by gas, Q = heat supplied by the gas.

2)  Air expands polytropically in a cylinder from a pressure of 1400 kPa, a temperature of 150oC., and a volume of 60 dm3, to a volume of 180 dm3, the index of expansion being, n= 1.2.  The adiabatic index for air, gamma = 1.4.

Calculate: a) The air temperature after expansion.

b) The amount of heat flow through the cylinder wall.

Ans:  66.56oC Ref DOT 26

Ans: 41.43 kJ

27. 1) Derive an expression for the external work done by a gas during a steady flow frictionless adiabatic expansion involving no change of kenetic or potential energy.

2) Oxygen flows at a steady rate of 10 kg/s through a open system, expanding adiabatically from an initial pressure of 9000 kPa and a temperature of 200oC to a final pressure of 3000 kPa. Assuming frictionless flow and no change in the kinetic and potential energy of the gas,  Calculate:

a) The final temperature of the oxygen.

b) The work flowing from the system per minute.

note: Universal gas constant, Ro = 8.3143 kJ(molK)-1, Relative atomic mass of Oxygen = 16, Specific heat capacity of Oxygen, Cp = 0.917 kJ(kgK)-1

Ans: W= m Cp (T1-T2)

Ans: 346.54K  73.54oC

Ans: 69.58 MJ/min

28.  One m3 of air initially at a pressure of 100 kPa at temperature of 15oC is compressed polytropically to a pressure of 1400 kPa.  Calculate:

1) the volume and temperature at the end of compression

2) the work done in compressing the air (kJ)

3) the change in internal energy (kJ)

4) the heat exchange through the cylinder walls (kJ)

note: the compression index n = 1.3

note: R(air) = 0.287 kJ(kgK)-1

note: specific heat capacity at constant pressure Cp = 1.005

Ans: 0.1314 m3 Ref DOT28

Ans: 256.8oC

Ans: -279.86 kJ

Ans: 210.1 kJ

Ans: -69.76 kJ

29.  A gasoline engine has a cylinder diameter of 100 mm and a stroke of 130 mm.  The pressure and temperature at the beginning of compression is 100 kPa and 57oC respectively, and the clearance volume is 230 cm3.  The law of compression is PV1.3 = C. Calculate:

1) the temperature at the end of compression

2) the work done on the gas during the compression stroke

Ans: 275.5oC Ref DOT29

Ans: -0.276 kJ

30. 1) Derive the following relationship for a polytropic process:  n-1

T2  = (p2) n  = (V1)n-1

T1    (p1)      (V2)

2) one kg of a certain gas expands adiabatically in a closed system until its pressure is halved. During the expansion the gas does 67 kJ of external work and its temperature falls from 240oC to 145oC. Calculate:

a) the value of the adiabatic index

b) the characteristic gas constant

Ans: See Reeds p73 and p74

Ans: gamma = 1.4194

Ans: 0.2958 kJ(kgK)-1

31.  A high speed diesel motor is in the design stage.  It is to be a 6 cylinder, 4 stroke cycle square engine. (cylinder dia. = stroke). It must develope 76 kW. at 2000 rev/min. with a mechanical efficiency of 80% and a mean effective pressure of 700 kPa. Calculate the cylinder dimensions.

Ans: Cylinder diameter and stroke = 120 mm

Ref DOT 31 Ref Reeds p109

32.  During a Morse test on a 4 cylinder internal combustion engine mounted on a test bed, the brake specific fuel consumption is 0.33 kg(kWh)-1 and the enfine developes a brake power of 40 kW. with all cylinders functioning. The speed is maintained constant at 30 rev/s. and with each

cylinder  cut out in turn, the average torque developed by the three remaining cylinders is 150 Nm.  The heating value of the fuel used = 40 MJ/kg. Calculate:

a) The indicated power.

b) The specific fuel consumption per indicated kWh.

c) The indicated themal efficiency.

Ans: 46.92 kW             Ref DOT32

Ans: 0.2813 kg/kWh(ind)

Ans: 31.99%

33.  Some modern motor vessels have been fitted with electronic devices employing a cathode ray oscilloscope for obtaining indicator diagrams from the cylinders of the main prime mover and displaying the results in a remote position such for example, as the Chief Engineers Office.  Describe such a device and state the manner in which it may be used to illustrate certain important features such as the compustion process etc.

Ans: See "Applied thermodynamics for Engineering

Technologists" 2nd edition (1974) pages 700- 704 and 766- 770

Ref DOT33

34. 1) Briefly describe the Morse Test as a method of obtaining the indicated power of a high speed, multi-cylinder gasoline engine.

2) An 8 cylinder gasoline engine operating on a test bed developed 240 kW at 50 rev/s. When one cylinder was cut out by shorting the spark plug, the brake power reduced to 200 kW.

Calculate the indicated power of this engine.

Ans: 320 kW

35.  The following data pertains to a 4 cylinder 4 stroke cycle, single acting compression ignition engine mounted on a test bed

mean effective pressure = 750 kPa    brake load   = 6kN

speed ................. = 4 rev/s    brake radius = 960mm

cylinder diameter ..... = 320mm      brake cooling water

stroke ................ = 480mm            inlet  = 14oC

outlet  = 47oC

specific fuel consumption (indicated) .......... = 49.5 kg/h

heating value of the fuel ...................... = 43.0 MJ/kg

specific heat capacity of cooling water ... = 4.187 kJ(kgK)-1

mass flow of cooling water ................ = 77.0 kg/min

Calculate:

1) the indicated thermal efficiency

2) the brake thermal efficiency

3) the heat balance diagram for this engine

Ans: 39.1% Ref DOT35

Ans: 24.49%

Ans:            100% heat energy supplied by fuel

!

_                    !                       _

!                     !                        !

I.P.  39.1%             Cooling water           Exhaust gas

!                    30.1%                   30.8%

_    !         _

!                !

B.P.          mechanical

24.49%        friction etc.14.61%

36.  The following data pertains to a single-cylinder, single-acting, two stroke cycle, diesel engine mounted on a test bed:

Mean effective pressure = 890 kPa.

Speed                   = 2.3 revs/s.

Cylinder diameter       = 360 mm.

Stroke                  = 780 mm.

Specific fuel consumption (brake) = 0.251 kg(kWh)-1

Calorific value         = 41.5 MJ/kg.

Calculate:

1) The indicated power.

2) The brake power.

3) The indicated thermal efficiency.

4) The total heat energy lost per second.

Ans: 162.52 kW           Ref DOT36

Ans: 144.5 kW

Ans: 38.87%

Ans: 255.6 kJ/s

37. A Carnot engine is operated between two heat resevoirs held at temperatures of 400 K and 300 K respectively.

1) Calculate the amount of energy (kJ) rejected to the sink if the engine receives 1200 kJ of energy at 400 K.

2) If the engine is now operated on the reversed Carnot cycle (refrigerator) and receives 1200 kJ of energy at 300K, calculate the quantity of energy delivered to the resevoir at 400 K.

3) Calculate the work done (kJ) in driving the compressor of part (2).

Ans. 1) Q = 900  kJ

Ans. 2) 1600  kJ

Ans. 3) 400  kJ

38.  A high speed compression ignition engine operating on the dual combustion cycle receives 2/3 of the total heat energy at constant volume and the remaining 1/3 of the energy

at constant pressure. Calculate: The temperatures (K) at the five cardinal points

of the cycle.

NOTE:

Compression ratio........ = 13:1

Maximum cylinder pressure = 5000 kPa

Air intake pressure...... = 100 kPa

Air intake temperature... = 15oC

Specific heat capicity at constant volume Cv = 0.71kJ(kgK)

Specific heat capacity at constant pressure Cp = 1.005kJ(kgK)

Ans: 288 K

Ans: 803.5 K

Ans: 1107 K

Ans: 1214 K

Ans: 451.5 K

39. An internal combustion engine operates on the dual-combustion cycle with a compression ratio of 10.7 : 1. Initially the pressure and temperature of the air at the start of the compression stroke are 100 kPa and 32oC, and the maximum pressure and temperature during the cycle are 4200

kPa and 1600oC respectively. Assume adiabatic compression and expansion. Calculate:

1) The pressures and temperatures at the remaining cardinal points of the cycle.

2) The ideal thermal efficiency.

note:

Specific heat capacity at constant volume, Cv = 0.718

kJ (kgK)-1 Specific heat capacity at constant pressure,

Cp =1.005 kJ (kgK)-1

Ans: 2761.5 kPa       787.2 K (514.2oC)

Ans: 1197.26 K  (924.26oC)     284.47 kPa   867.64 K  (595oC)

Ans: 58.49%

40. 1) Sketch the pressure - volume diagram for the ideal Carnot cycle.  Describe the sequence of events in a perfect reciprocating heat engine operating on the cycle and derive an expression for the cycle efficiency.

2) Determine the Carnot efficiency of:

a) a gasoline motor operating within the temperature limits of 80oC and 2080oC

b) Skinner uniflow engine supplied with steam at a pressure of 2000 kPa and a temperature of 260oC exhausting to a condenser at a pressure of 7 kPa

Ans: See Reeds p135 - p137

Ans: 85%

Ans: 41.46%

41.  An internal combustion engine operates on the constant volume cycle with a compression ratio of 7:1.  Another engine, operating on the diesel cycle, has a compression ratio of 16:1 the fuel being admitted at constant pressure for 6% of the stroke.  Compare the air standard efficiencies (A.S.E) of the two engines by means of the following

formulae:

1. constant volume cycle A.S.E. =  1 -   1 / r(gamma-1)

2.  Diesel cycle .  = 1-(  1  ) (  1  )     {rho (gamma-1}/(gamma) (r(gamma-1) {rho -1}

note: r = compression ratio

note: rho = fuel cut-off ratio

note: gamma = 1.4 (adiabatic index for air)

Ans: 54.08%              Ref DOT41

Ans: 61.89%

42. With a internal combustion engine operating on the constant volume cycle, the pressure, volume, and temperature at the start of the compression stroke are 99 kPa, 113 dm3 and 48oC respectively, the compression ratio being 10:1. The gas receives 95 kJ of energy during the combustion process, the law of compression is pv 1.37 = C, the specific heat capacity at constant volume is 0.712 kJ (kgK)-1 and the characteristic gas constant  R = 0.29 kJ (kgK)-1.  Calculate:

1) The mass of gas compressed during the cycle.

2) The pressure and temperature at the end of compression.

3) The pressure and temperature at the end of combustion.

Ans: 0.1202 kg

Ans: 2320.8  kPa     752.5K    479.5oC

Ans: 5744.2  kPa    1862.5K   1589.5oC

43.  A single stage, double acting compressor rotating at 300 rev/min delivers air at the rate of 14 m3/min. The suction conditions are 101.3 kPa and 15oC with delivery pressure of 700 kPa.  The clearance volume is 5% of the swept volume and the compression index n = 1.3.  Calculate:

1) the air temperature at delivery from the cylinder

2) the volume swept out by the piston (m3)

3) the indicated power (kW)

Ans: 176.9 Ref DOT43

Ans: 0.0281 m3

Ans: 57.58 kW

44.  Air is compressed in a single stage reciprocating compressor from a pressure of 101.3 kPa and a temperature of 15oC to the delivery pressure of 700 kPa.  Calculate the indicated power required for a free air delivery of 0.3 m3/min when the compression process is:

1) isentropic

2) reversible isothermal

3) polytropic, with n = 1.25

Ans: 1.31 kW Ref DOT44

Ans: 0.979 kW

Ans: 1.195 kW

45.  A three stage single acting compressor having a free air delivery of 2.83 m3/min operates in a situation where the atmospheric pressure is 101.3 kPa and the air temperature is 15oC.  The suction air pressure and temperature are 98 kPa and 32oC respectively.  The delivery presssure is 7000 kPa the compression index, n = 1.3 and R(air) = 0.287 kJ(kgK)-1. Calculate the indicated power required for the process assuming complete intercooling between stages and that the machine is designed for minimum work.          n-1

note: total indicated work = Z  _n_  mRT1 [{p2}zn  -1 ]

n-1       [{p1}       ]

note: Z = number of stages

note: m = mass air delivered

note: n = compression index

Ans: 24.14 kW

46) A single-acting single-stage, reciprocating air compressor absorbs 14 kW with a mean piston speed of 3 m/s and a rotation speed of 6.0 rev/s. Air is asperated into the cylinder at 100 kPa and compressed to 2000 kPa, the compression index, n = 1.32 , neglecting the effect of

clearance, Calculate:

1) The stroke of the compressor piston.

2) The diameter of the compressor cylinder.

3) The mean effective pressure.

note: For a polytropic operation, W = P1V1-P2V2 / n-1

Ans: 250mm

Ans: 164.3mm

Ans: 440.33 kPa

47.  Air at a pressure of 98 kPa. and a temperature of 18oC is aspirated into a two stage compressor at the rate of 0.05 kg per stroke.  The air leaves the first stage at a pressure of 295 kPa and is then passed through an intercooler where it is cooled at constant pressure to the initial temperature. The air is further compressed in the second stage to a pressure of 730 kPa and again passed through a cooler where the temperature is once more reduced to the initial state. Calculate:

1) The % decrease in volume due to cooling at the end of each stage.

2) The % decrease in volume if compression had occured in a single stage and then cooled to the initial temperature.

R (air) = 0.287 kJ(kgK)-1

pVn = Constant, where n = 1.3 for each stage.

Ans: 22.47%

Ans: 18.87%

Ans: 37.1% Ref.   DOT 47.

48.  Air is aspirated into the cylinder of a single stage air compressor at a pressure of 100 Kpa a temperature of 25oC and delivery at pressure of 600 kPa.  The volume swept out by the

piston amounts to 1440 cm3 and the clearance volume equals 40 cm3. If the compression index, n = 1.3 Calculate:

1) the fraction of the stroke when the delivery valves open

2) the fraction of the stroke when the suction valves open

3)  the mean effective pressure

note: for a polytropic operation W = P1V1 - P2V2, including clearance n-1

Ans: 0.76875 Ref DOT48

Ans: 0.08243

Ans: 203.57 kPa

49.  Air is compressed in the cylinder of a compressor according to the law PVn = C.  The initial condition of the air is 100 kPa 20oC and 0.125 m3 and the final condition 3800

kPa and 510oC.

note: the specific heat capacity Cp = 1.005 kJ(kgK)-1 the specific heat capacity Cv = 0.718 kJ(kgK)-1. Calculate:

1) the compression index

2) the mass of air compressed

3) the work done during compression

4) the change of internal energy

Ans: 1.37 Ref DOT49

Ans: 0.1486 kg

Ans: -56.48 kJ

Ans: 52.28 kJ

50. A single acting,single stage, air compressor aspirates air at 100 kPa and delivers at 600 kPa. The cylinder is 300 mm diameter, the stroke 425 mm and it operates at 5 rev/s.  Initially the compressor index was 1.15 but after operating for some period of time the index was found to be 1.35. Neglecting the effect of clearance, Calculate:

1) The power absorbed in each case.

2) The % increase in the power absorbed by the compressor.

n-1

Note: Work per cycle = _n_ P1V1 [{P2} n -1]

n-1      [{P1}     ]

Ans: 30.16  kW

Ans: 34.2  kW

Ans: 13.3%

51. The pressure and temperature in a stream condenser is 9 kPa. and 40oC.  The dryness fraction of the steam is 0.86. Find the mass ratio of steam to air present in the condenser.

NOTE: R(air) = 0.287kJ(kgK)-1.

Ans. 3.3:1 Ref DOT 51

52.  A vessel of volume 8.7 m3 contains air and dry saturated steam at a total pressure of 6.24 kPa and temperature 30oC. Taking R(air) as 0.287 kJ(kgK)-1 Calculate:

1) the mass of steam in the vessel

2) the mass of air in the vessel

Ans: 0.2642 kg Ref DOT52

Ans: 0.2 kg

53.  In a steam turbine plant, the condenser vacuum is equivalent to 685 mm. of mercury when the atmospheric pressure indicated with a mercurial barometer is 760mm. The fluid temperature at the extraction outlet is 39oC. and R(air) = 0.287 kJ(kgK)-1. Calculate:

1) the specific volume of the extracted air.

2) the quantity of vapour (kg) removed with each kg. of air extracted with the ejector.

Ans: 29.87 m3/kg Ref DOT53

Ans: 1.45 kg

54.  A throttling calorimeter was employed to provide information upon the quality of steam passing through a pipeline.  The following data was recorded: steam pressure in pipeline = 1100 kPa, steam pressure after passing through orifice = 100 kPa. Calculate the minimum dryness fraction that can be measured for these particular conditions.

Ans: 0.94786 Ref DOT54

55.  A combined throttling / separating calorimeter was employed to provide information upon the quality of steam passing through a pipeline.  The following data was recorded:

pipeline pressure................. = 1000 kPa

throttling calorimeter pressure... = 120 kPa temperature = 109.8oC

quantity of water collected after throttling = 3.03 kg

quantity of water collected in separator = 0.113 kg

specific heat capacity of superheated steam at calorimeter

pressure = 2.02 kJ(kgK)-1

Calculate the dryness fraction of the steam

Ans: 0.9244 Ref DOT55

56.  Superheated steam at a temperature of 260oC and a pressure of 1500 kPa is mixed in the mass ratio of 2 to 3 (superheated steam to wet steam) with steam at the same pressure but of dryness fraction 0.88.  The mixture is then throttled through a reducing valve to a pressure of 800 kPa.

Assume no losses occur, calculate the dryness fraction of the steam:

1) after mixing but before throttling

2) after throttling

Ans: 0.96 Ref DOT56

Ans: 0.973

57.  Using the following formula, calculate the entropy per kg. of superheated steam at 1500 kPa and 300oC. taking the mean specific heat of water and superheated steam as 4.24 and 2.43 kJ(kgK)-1 respectively.  Compare result with the value given in the steam tables. s = C(w) ln T(sat) + hfg   + C(sup) ln T

273      T(sat)            T(sat)

C(w)   = mean specific heat of water

C(sup) = mean specific heat of superheated steam

T(sat) = saturation temperature absolute

T      = superheated steam temperature absolute

Ans. s = 6.9172 kJ(kgK)-1       Ref DOT57

Ans: Using A.S.M.E. Steam Tables: s = 6.9207 kJ(kgK)-1

58.  1 kg of superheated steam at 8000 kPa and 520oC is throttled to a pressure of 1000 kPa then expanded at constant entropy to a pressure of 2 kPa.  Using the enthalpy - entropy

(h-s) chart calculate:

1) the change in enthalpy

2) the change in entropy

3) the dryness fraction at 2 kPa

Ans: 1200 kJ(kg)-1       Ref DOT57

Ans: 0.93 kJ(kgK)-1      Ref MAR84

Ans: 0.885               Ref Mc Conkey p424

59. 1) Sketch in diagramatic form, a simple gas-turbine generator plant showing the compressor, combustor, turbine and generator.

2) Sketch a temperature/entropy diagram for this cycle indicating the adiabatic irreversible/isentropic operations with solid lines and the effect of blade friction (adiabatic irreversible phenomena),with broken or dotted lines.

3) Air at a temperature of 15oC and a pressure of 100 kPa enters the compressor of the above plan which has a maximum cycle temperature of 600oC and a pressure ratio of 6/1.

The isentropic efficiencies of the compressor and the turbine are 0.82 and 0.85 respectively.   Calculate:

a) The actual temperature at the end of compression.

b) The actual temperature at the end of expansion.

Note: Adiabatic index, gamma = 1.4

Ans.3a) 523.36K  250.36oC

Ans.3b) 575.7K  302.7oC

60.  During a certain type of process dry saturated steam at a pressure of 4000 kPa is throttled to 500 kPa and then allowed to expand isentropically to a pressure of 60 kPa. Using the enthalpy - entropy (h-s) chart calculate:

1. the change in entropy during this process

2. the final condition of the steam after the expansion has occured

Ans: 0.871 kJ(kgK)-1     Ref DOT60

Ans: 9.2%                Ref MAY84

61.  A turbine is supplied with steam at a pressure of 6000 kPa and a temperature of 540oC.  Isentropic expansion occurs as the steam passes through the turbine until the exhaust pressure of 6 kPa is reached. Using the enthalpy-entropy (h-s) chart, calculate:

1) the dryness fraction at the end of the expansion process.

2) the Rankine efficiency.

Ans: 0.83               Ref DOT61

Ans: 40.37%

62. 1) Sketch a flow diagram for a simple saturated steam turbine plant using numbers to denote the cardinal points of the cycle

2) Illustrate the Rankine cycle for this process with a pressure / volume (pV) diagram and a temperature / entropy (Ts) diagram.  Use the same numbers used in part (1) to indicate the main points of these diagrams.

Ans:? Ref DOT62

63.  A double acting compound steam engine develops an indicated power of 500 kW using dry saturated steam at a pressure of 1400 kPa and exhausting to atmospheric at pressure of 100 kPa. The overall expansion ratio is 12:1 and the cut off ratio in the high pressure cylinder is 1:3.  The diagram factor for the engine is 0.8 and the piston speed is 250 m/min.  Assume hyperbolic expansion in each cylinder. Calculate:

1) the high pressure cylinder diameter

2) the low pressure cylinder diameter

Ans: 790 mm Ref DOT63

Ans: 395 mm Ref Mar84

64. A double acting single cylinder steam engine developes 70 kW at 250 rev/min using dry saturated steam supplied at a pressure of 1100 kPa and exhausting into a condensor at 75 kPa. The cut off ratio is 0.25 and the stroke/bore ratio is 1.3 / 1. The mechanical efficiency = 85%, and the affect of the piston rod may be neglected. ON the basis of a hypothetical diagram, Calculate:

1) The bore and stroke of the engine assuming a diagram factor of 0.8.

2) The specific steam cosumption of the engine if the brake thermal efficiency is 15%

Ans. 275 mm   358 mm

Ans.10.02 kg/kWh

65.  The travel of a slide valve is 32 cm and the lap is 7 cm.  When the crank has passed through 90o from the dead centre position, the port opening is 7 cm. Find the lead either graphically or by calculation.

Ans: 7.5 mm Ref  DOT65

66.  A steam engine uses steam at the rate of 13.3 Mg/h when developing an indicated power of 1.5 MW , and uses 18.7 Mg/h when developing an indicated power of 2.25 MW. Calculate:

1) Willams Law for this engine.

2) the steam consumption (Mg/h) when developing 2000 kW.

3) the specific consumption, kg(kWh)-1 when developing 2000 kW.

Ans: m = 2.5 + 7.2 P

Ans: 16.9 Mg/h Ref DOT66

Ans: 8.45 kg/kWh

67.  Steam is supplied to the high pressure cylinder of an engine at a pressure of 1500 kPa. and cut-off takes place at 45% of the stroke.  The exhaust pressure is 650 kPa., the clearance volume equals 10% of the stroke volume, and compression begins when the piston has travelled 88% of the exhaust stroke.  Assume isothermal conditions to prevail to the end of the expansion and compression strokes.

1) Sketch the indicator diagram showing the given data.

2) Calculate the mean effective pressure.

Ans.  mep = 562.1 kPa

68. An engine is supplied with steam at a pressure of 1500 kPa and a temperature of 260oC, the exhaust pressure being 16 kPa.  Assumming isentropic expansion,  Calculate:

1) The dryness fraction of the steam after expansion

2) The Rankine efficiency.

Ans.0.829

Ans.27.6%

69. Dry saturated steam at a pressure of 1500 kPa is expanded through a turbine nozzle to a pressure of 900 kPa, the expansion following the law PV1.135 = C.  Calculate:

1) The dryness fraction of the steam as it leaves the nozzle.

2) The change of enthalpy of the steam during the passage through the nozzle. (kJ/kg)

3) The velocity of discharge.

4) The nozzle exit (mm2) for a mass flow of 1 kg/s

Ans: 0.961

Ans: 96.95  kJ/kg

Ans: 440.34  m/s

Ans: 469  mm2           Ref  Reeds pg234

70.  In a reheat turbine cycle, steam, at a pressure of 5000 kPa and a temperature of 460oC expands through the first stage turbine to a pressure of 300 kPa.  The steam is then passed through the reheater where the temperature is raised to its original value while the pressure remains constant at 300 kPa.  The steam now passes through the final stage where it expands to the condenser pressure of 3 kPa.  Calculate the Rankine efficiency assuming an ideal reheat cycle.

Ans: 41.2% Ref DOT70

71. The theoretical change of enthalpy of the steam during its passage through the nozzles of an impulse turbine is 312.5 kJ/kg, and of this, 10% is lost due to friction. The nozzles are inclined at 20o to the plane of the wheel. The inlet angles of the blades is 35o and the absolute velocity of the steam leaving the blades is 204 m/s in the direction of the turbine axis.  Assuming steam is supplied to the machine at the rate of 1 kg/s,  Calculate:

1) The blade velocity to avoid shock at entry.

2) The exit angle of the blades.

3) The power developed (kW)

Ans.338.?  m/s

Ans.31.076o

Ans.238.6  kW

Ans.84.82%

72.  Steam from the nozzle of a single stage impulse turbine impinges upon the bleads from an angle of 18o to the plane of the wheel and with a velocity of 900 m/s.  The linear velocity of the blades is 330 m/s and the steam consumption is 0.095 kg/s.  The blades are symmetrical and have a frictional loss of 10%. Calculate:

1) the tangenial force on the blades (N)

2) the power developed (kW)

3) the axial thrust due to the steam (N)

Ans: 94.93 N Ref DOT72

Ans: 31.32 kW Ref FEB84

Ans: 2.641 N Ref MAR84

73.  Steam is supplied to a turbine at a pressure of 2000 kPa and a temperature of 440oC.  It exhausts to the condenser at a pressure of 4 kPa. and dryness fraction is 0.85. 14.0% of the steam passing through the turbine is extracted for feed water heating at a pressure of 150 kPa.

Calculate:

1) the thermal efficiency without feed heating.

2) the thermal efficiency with feed heating.

Ans: 35.66%

Ans: 38% Ref DOT 73

74.  Air at a pressure of 100 kPa and 20oC is aspirated into a gas turbine plant operating on the constant pressure cycle and discharged to the combustion chamber at 600 kPa. The gases entering the turbine are at a temperature of 900oC and both compression and expansion can be assumed to be adiabatic.  If the specific heat capacities Cv = 0.718 kJ(kgK)-1 and cp = 1.005 kJ(kgK)-1 calculate:

1) the temperature at the end of compression

2) the temperature of the exhaust

3) the energy transfer at constant pressure (kJ/kg)

4) the increase of internal energy from inlet to exhaust (kJ/kg)

5) the ideal thermal efficiency

Ans: 216oC               Ref DOT74

Ans: 430oC

Ans: 687.4 kJ/kg

Ans: 294.4 kJ/kg

Ans: 40.06%

75. An Orsat apparatus was used to analyze the exhaust from a gasoline engine.  The results, on a volumetric basis, were as follows: CO2= 12.5% ; O2 = 3.1% ; CO = 0.5%. Convert this analysis to a mass analysis and determine the mass of 100m3 of the exhaust gas at 15oC and 100 kPA.

Ans: 125.83 kg Ref DOT 75.

76. The coal used for firing a power station boiler has an analysis by mass of: C = 81% , H2 = 4.5% , and 02 = 3.5%, the remainder being ash. Calculate:

1) The theoretical mass of air required for complete combustion of 1 kg of this fuel.

2) The percent analysis by mass and by volume of the flue gases formed when the fuel is burnt with 65% excess air.

3) The density of the flue gases at a pressure of 100 kPa and a temperature of 0oC.

Ans:  10.8  kg

Ans:  C02 m= 15.88%  v= 10.68%

H20 m=  2.16%  v=  3.56%

02  m=  8.63%? v=  8.01%

N2  m= 73.33%  v= 77.75%

Total =100.00%    100.00%

Ans:  1.308  kg/m3

77.  The volumetric composition of air is : Oxygen = 21%, nitrogen = 79%.  The volumetric composition of a particular gasious fuel is a follows: H2= 48%  CH4= 21%  C6H6= 1.5%  CO= 19%  N2= 6%  CO2= 4.5%. The correct quantity of air is supplied so that perfect combustion takes place. Calculate:

1) the contraction in volume (% basis) due to combustion.

2) the volumetric air/gas ratio.

3) the volumetric analysis (% basis) of the combustion products.

Ans: 6.43% Ref DOT77

Ans: 4.13:1

Ans: Products    k mol     %k mol

CO2       53.5       11.14

H2O       94.5       19.69

N2       332.0       69.17

Total    480.0      100.00

78.  A 50 ml (millilitre) sample of lake Ontario water required 6.2 ml of a certain reagent to indicate the end point that is the hardness of the sample.  The reqgent is equivalent to 6.2 mg of Calcium Carbonate (CaCO3). Calculate the hardness of a 1000 ml sample of this water and express the result in parts per million (p.p.m.)

Ans: 124 p.p.m. Ref DOT78

79.  A two stroke diesel motor develops an indicated power of 3000 kW with a specific fuel consumption (indicated) of 0.225 kg(kWh)-1.  The combustion of 1 kg of fuel requires 18 kg of

air.  The exhaust gases from the motor pass through a boiler, entering at a temperature of 330oC and leaving at a temperature of 215oC, the gasses having a specific heat capacity of 1.05 kJ(kgK)-1.  Steam is generated in the boiler at a pressure of 1500 kPa and a dryness factor of 0.97.  The feed water is at a temperature of 50oC and the boiler efficiency is 0.8.  Calculate the quantity of steam generated per hour.

Ans: 491.2 kg/h Ref DOT79

80.   Steam is generated in a boiler at the rate of 50000 kg/h, at a pressure of 4000 kPa and a temperature of 460oC. The daily consumption amounts to 88 tonnes of fuel having a heating value of 41 MJ/kg.  The overall plant efficiency is 16%, and the feed water temperature is 150oC.  Calculate:

1) the boiler efficiency

2) the equivalent power output of the turbine

3) the boiler evaporation rate (kg/h) from and at 100oC

4) the equivalent (kg of steam/kg of fuel) from and at 100oC.

Ans: 90.53% Ref DOT80

Ans: 6681 kW

Ans: 60299 kg/h

Ans: 16.445 (kg steam/kg fuel)

81.  Sketch a temperature - entropy (T-s) diagram for a vapour compression refrigeration system indicating the effect of:

1) isentropic compression to a superheated state

2) undercooling of the liquid refrigerant during the condensing process Sketch a pressure - enthalpy (p-h) diagram for a vapour compression refrigeration system indicating the effect of :

a) isentropic compression to a superheated state

b) undercooling of the liquid refrigerant during the condensing process

Ans: diagram Ref DOT81

82.  The pressure and temperatures of the refrigerant entering and leaving the compressor of an R-12 system are 150.9 kPa and -5oC and 491.4 kPa and 45oC respectively. The refrigerant leaves the condenser as a saturated liquid at 15oC.  Calculate the coefficient of performance of the

system.

Ans: 5.175 Ref DOT82

83.  The pressure and temperature of the refrigerant entering the compressor of an R-12 system is 182.6 kPa and 0oC, and entering the condenser, 567.3 kPa and 50oC, respectively. The refrigerant leaves the condenser as a saturated liquid at a pressure of 567.3.  Calculate the coefficient of performance.

Ans: 5.085 Ref DOT83

84. The pressure and temperature of the refrigerant entering the condenser of an ammonia system is 1470 kPa and 63oC respectively, and it leaves at the same pressure with no undercooling. The gas enters the compressor at 207.7 kPa and compression is isentropic with a flow rate of 0.15 kg/s. Calculate:

1) The refrigerating effect

2) The work transfer in the compressor

3) The coefficient of performance.

Ans: 140.94  kW

Ans: 36.6975  kW

Ans: 3.84 Ref DOT84

85.  The pressure and temperature of the refrigerant entering the condenser of an R-12 system is 1219 kPa. and 65oC respectively, and it leaves as a saturated liquid at the same pressure. The gas enters the compressor at 80.71 kPa and compression is isentropic with a flow rate of 15 kg/min. Calculate:

1) the refrigeration effect.

2) the coefficient of performance.

Ans: 1285.35 kJ/min Ref DOT85

Ans: 1.785

86.  A refrigerator is driven by a 2.25 kW motor and yields ice at the rate of 2.5 tonnes per day.  The ice is at a temperature of -7oC and is produced from water at a temperature of 18oC.  Calculate:

1) the coefficient of performance of the machine

2) the capacity (tonnes/day) from and at 0oC

note: specific heat capacity of water = 4.2 kJ(kgK)-1

note: specific heat capacity of ice   = 2.04 kJ(kgK)-1

note: enthalpy of fusion (ice) = 335 kJ/kg

Ans: 5.464 Ref DOT86

Ans: 3.171 tonnes/day

87.    A steam engine uses steam at the rate of 13,3 Mg/h when developing an indicated power of 1,5 MW, and uses 18,7 Mg/h when developing an indicated power of 2,25 MW. Calculate:
i) Willan's Law for this engine;
ii) the steam consumption (Mg/h) when developing 2 000 kW;
iii) the specific consumption, (kg/kW-h) when developing 2 000 kW.

88.    Steam at a pressure of 3 000 kPa and a temperature of 500C flows through a 150 mm diameter pipe which is covered with lagging to a diameter 300 mm. The temperature of the outer surface of the lagging is 50C and the thermal conductivity coefficient of the lagging is 0,6 W/mK. Calculate the energy lost per second from a 50 m lenght of pipe.

89.    Steam is supplied to a turbine at a pressure of 2 000 kPa and a temperature of 440C. It exhausts to the condenser at a pressure of 4 kPa and dryness fraction 0,85. 14,0% of the steam passing through the turbine is extracted for feed water heating at a pressure of 150 kPa. Calculate:
i) the thermal efficiency without feed heating;
ii) the thermal efficiency with feed heating.

90.    Superheated steam at a temperature of 260C and a pressure of 1 500 kPa is mixed in the mass ratio 2/3 (superheated steam to wet steam) with steam at the same pressure but of dryness fraction, 0,88. The mixture is then throttled through a reducing valve to a pressure of 800 kPa. Assume no losses occur, calculate the dryness fraction of the steam:
i) after mixing but before throttling;
ii) after throttling.

91.    Linear expansion coefficients:
Aluminum = (22,5) (10-6) /K
Nickel = (12,8) (10-6) /K
Brass = (18,0) (10-6) /K

92.    A condenser has a volume of 20 m3 and contains a mixture of air and dry saturated steam at a total pressure of 9 kPa and a temperature of 38C. Calculate:
i) the mass of steam in the vessel;
ii) the mass of air in the vessel;
iii) the mass ratio of air to steam in the vessel.

NOTE: R(air) = 0,287 kJ/kgK

93.    Air is compressed in the cylinder of a compressor according to the law PVn = C. The initial condition of the air is 100 kPa, 20C and 0,125m3 and the final condition, 3 800 kPa and 510C. The specific heat capacities are:
Cp = 1,005 kJ/kgK
Cv = 0,718 kJ/kgK
Calculate:
(i) the compression index;
(ii) the mass of air compressed;
(iii) the work done during compression;
(iv) the change of internal energy.

94.    The following data pertains to a 4 cylinders, 4 stroke cycle, single acting compression ignition engine mounted on a test bed:
Mean effective pressure = 750 kPa
Speed = 4 rev/s
Cylinder diameter = 320 mm
Stroke = 480 mm
Brake cooling water, inlet = 14C
Brake cooling water, outlet = 47CSpecific fuel consumption (indicated) = 49,5 kg/h
Heating value of fuel = 43,0 MJ/kg
Specific heat capacity of cooling water = 4,187 kJ/kgK
Mass flow of cooling water = 77 kg/min.

Calculate:
(i) the indicated thermal efficiency;
(ii) the brake thermal efficiency;
(iii) the heat balance diagram for this engine.